Solving Systems Using Elimination Chapter 7 Section 3 Solving Systems Using Elimination

When both equations are in Ax + By = C form you can solve by using elimination *make sure both equations are in Ax + By = C form Steps Make either the x or y term additive inverses, if necessary Combine the 2 equations Solve for the variable that remains Pick one equation Substitute the value of the variable you solved for Find the value of the 2nd variable

*make sure both equations are in Ax + By = C form Example 1 Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 √ 5x – 6y = -32 3x + 6y = 48 8x = 16 8 8 x = 2 5x – 6y = -32 5(2) – 6y = -32 10 – 6y = -32 –10 –10 -6y = -42 -6 -6 y = 7 The solution is (2,7)

The solution is (89,203), 89 adult, and 203 student Example 2 Suppose your community center sells a total of 292 tickets for a basketball game. An adult ticket costs $3. A student ticket costs $1. The sponsors collect $470 in ticket sales. Write and solve a system to find the number of each type of ticket sold. a + s = 292 3a + s = 470 -1(a + s = 292) -a – s = -292 Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 √ -a – s = -292 3a + s = 470 2a = 178 2 2 a = 89 a + s = 292 89 + s = 292 –89 –89 s = 203 The solution is (89,203), 89 adult, and 203 student

The solution is (-4,-1/2) Example 3 9a = 72b –72b –72b 9a – 72b = 0 Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 √ 9(-5a + 14b = 13) 5(9a – 72b = 0) -5a + 14b = 13 9a – 72b = 0 9a = 72b 9a = 72 (-1/2) 9a = -36 9 9 a = -4 -45a + 126b = 117 45a – 360b = 0 -234b = 117 -234 -234 b = -1/2 The solution is (-4,-1/2)

Questions? Ask now!

Assignments Class Work Page 390 – 392 #1 – 16, 17 – 37 odd Homework Finish Class Work; Page 393 #51 – 56